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Collinear double-pulse seeding of the High-Gain Harmonic Generation (HGHG)process in a free-electron laser (FEL) is a promising approach to facilitatevarious coherent nonlinear spectroscopy schemes in the extreme ultraviolet(XUV) spectral range. However, in collinear arrangements using a singlenonlinear medium, temporally overlapping seed pulses may introduce nonlinearmixing signals that compromise the experiment at short time delays. Here, weinvestigate these effects in detail by extending the analysis described in arecent publication (Wituschek et al., Nat. Commun., 11, 883, 2020). High-orderfringe-resolved autocorrelation and wave-packet interferometry experiments atphoton energies > $23\,$eV are performed, accompanied by numerical simulations.It turns out that both the autocorrelation and the wave-packet interferometrydata are very sensitive to saturation effects and can thus be used tocharacterize saturation in the HGHG process. Our results further imply thattime-resolved spectroscopy experiments are feasible even for time delayssmaller than the seed pulse duration.

High-Gain Harmonic Generation with temporally overlapping seed pulses and application to ultrafast spectroscopy